The research by the Albert Shanker Institute, a think tank supported by the American Federation of Teachers, raises questions about whether districts are doing enough to hold on to their diverse teachers, who tend to work in higher-poverty schools.

Education scholars have long lamented a "teacher diversity" gap between the overwhelmingly White profession and an increasingly diverse student population, which is now more than half non-White. The new research shows that the supply of Black teachers poses a particular challenge.

The cities studied are Boston, Chicago, Cleveland, Los Angeles, New Orleans, New York, Philadelphia, San Francisco, and Washington. The New York, Los Angeles, and Chicago districts, in that order, are the three largest school systems in the United States. They serve about 1 million, 670,000, and 350,000 students, respectively.

Many of those cities studied have seen significant contraction in their student populations over the past decade, so some decline in the teaching population there was expected. But Black teachers were often much more heavily hit than other groups. In Cleveland, for example, the overall teaching force shrank by 17 percent between 2001 and 2011, but the percentage of Black teachers declined by 34 percent.

Then there's Philadelphia: The teaching force increased by 13 percent in Philadelphia over the 2001-2011 time period, but during this same period, the percentage of Black teachers dropped by 19 percent.

In the District of Columbia, the percent of Black teachers fell from 77 percent to 49 percent from 2003 to 2011.

The report is careful to note that it provides only descriptive figures rather than a causal explanation for the findings. But many potential theories are possible: The District of Columbia's population grew more White over this time period thanks to hyper-gentrification, possibly pushing Black teachers out into the suburbs as housing prices went up. In Cleveland, most of the loss of teachers of color occured at charter schools, the report notes, raising the possibility that the growth of those schools had an effect.

How these trends affect students also plays out differently, because of the varying demographics in the cities. In Philadelphia, the teacher-diversity gap for Black students actually closed during the period studied, despite the loss of so many Black teachers, because the number of Black students also declined.

In response to the report, AFT President Randi Weingarten called for a national summit to address teacher diversity in urban districts.

"Diversity is a key component to equality and opportunity. Where there's a diverse teaching workforce, all kids thrive. That's why we note with alarm the sharp decline in the population of Black teachers in our cities," she said.

Here's some more in-the-weeds information on the report:

How was the research conducted?

The Shanker Institute used open-records requests to gain information on the composition of the student population and the teaching force from each city's district. Because of differences in the specific data available and limitations particular to each collection, the data isn't strictly comparable from city to city. (An appendix spells out the specific methodology used to examine the results for each city.)

The data is pretty complex here, and there are a lot of ways to slice and dice it, so here are a couple of other visualizations.

Which of the districts has the greatest gap between the ethnic makeup of its teacher and student population?

That would be Philadelphia, where 31 percent of teachers are Black, Hispanic, or another race, but 86 percent of students are — a whopping 55 percentage-point difference. Following close behind are Cleveland (a 53 percentage-point diversity gap) and Boston (a 51 percentage-point gap).

Didn't the districts try to bring on more teachers of color over this time period?

It turns out that many of the districts don't seem to have been all that successful at this, particularly when it comes to Black teachers. The proportion of Black teachers among new hires in Chicago between 2003 and 2011 was "consistently and meaningfully lower" each year compared to Black representation among teachers the previous year. Consequently, the proportion of Black teachers dwindled from 38 percent to 27 percent over that time period.

It isn't clear whether this was due in part to a lack of qualified applicants of color — Black male teachers are in particularly short supply across the cities — or some other factor.

Is there any good news?

Los Angeles saw an increase of 6.5 percent in the proportion of its teaching force identifying as Hispanic, lowering the diversity gap for that population slightly. (Both White and Black teachers in the district decreased significantly, as did the teacher population as a whole.)

Overall, its hiring of candidates of color appears to have been more successful than that of other districts.

How does all this stack up nationally?

As of about 2011-12, 44 percent of U.S. students were nonwhite but only 17.3 percent of students teachers were, according to federal data presented in the report. (Today, more than half of all K-12 students are students of color.)

The report notes that, although nationally schools have done a better job recruiting teachers of color, the work remains challenging because such teachers have higher turnover rates, probably because of poor working conditions in the schools where they're concentrated.

The report concludes by offering recommendations for the federal government, states, and local districts and schools on how to increase teacher diversity.